(12-x)(20+x)=1750 eching

$$(12-x)(20+x)=1750$$

x uchun yechish (complex solution)

$$x=-3\sqrt{166}i-4\approx -4-38,65229618i$$

$$x=-4+3\sqrt{166}i\approx -4+38,65229618i$$

Kvadrat tenglamalaridan foydalanish qoidalari

12-x ga 20+x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$240-8x-x^{2}=1750$$

Ikkala tarafdan 1750 ni ayirish.

$$240-8x-x^{2}-1750=0$$

-1510 olish uchun 240 dan 1750 ni ayirish.

$$-1510-8x-x^{2}=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$-x^{2}-8x-1510=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -1 ni a, -8 ni b va -1510 ni c bilan almashtiring.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-1\right)\left(-1510\right)}}{2\left(-1\right)}$$

-8 kvadratini chiqarish.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-1\right)\left(-1510\right)}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64+4\left(-1510\right)}}{2\left(-1\right)}$$

4 ni -1510 marotabaga ko'paytirish.

$$x=\frac{-\left(-8\right)±\sqrt{64-6040}}{2\left(-1\right)}$$

64 ni -6040 ga qo'shish.

$$x=\frac{-\left(-8\right)±\sqrt{-5976}}{2\left(-1\right)}$$

-5976 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-8\right)±6\sqrt{166}i}{2\left(-1\right)}$$

-8 ning teskarisi 8 ga teng.

$$x=\frac{8±6\sqrt{166}i}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{8±6\sqrt{166}i}{-2}$$

x=\frac{8±6\sqrt{166}i}{-2} tenglamasini yeching, bunda ± musbat. 8 ni 6i\sqrt{166} ga qo'shish.

$$x=\frac{8+6\sqrt{166}i}{-2}$$

8+6i\sqrt{166} ni -2 ga bo'lish.

$$x=-3\sqrt{166}i-4$$

x=\frac{8±6\sqrt{166}i}{-2} tenglamasini yeching, bunda ± manfiy. 8 dan 6i\sqrt{166} ni ayirish.

$$x=\frac{-6\sqrt{166}i+8}{-2}$$

8-6i\sqrt{166} ni -2 ga bo'lish.

$$x=-4+3\sqrt{166}i$$

Tenglama yechildi.

$$x=-3\sqrt{166}i-4 x=-4+3\sqrt{166}i$$

Kvadratni yakunlash bo'yicha qadamlar

12-x ga 20+x ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$240-8x-x^{2}=1750$$

Ikkala tarafdan 240 ni ayirish.

$$-8x-x^{2}=1750-240$$

1510 olish uchun 1750 dan 240 ni ayirish.

$$-8x-x^{2}=1510$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$-x^{2}-8x=1510$$

Ikki tarafini -1 ga bo‘ling.

$$\frac{-x^{2}-8x}{-1}=\frac{1510}{-1}$$

-1 ga bo'lish -1 ga ko'paytirishni bekor qiladi.

$$x^{2}+\left(-\frac{8}{-1}\right)x=\frac{1510}{-1}$$

-8 ni -1 ga bo'lish.

$$x^{2}+8x=\frac{1510}{-1}$$

1510 ni -1 ga bo'lish.

$$x^{2}+8x=-1510$$

8 ni bo‘lish, x shartining koeffitsienti, 2 ga 4 olish uchun. Keyin, 4 ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}+8x+4^{2}=-1510+4^{2}$$

4 kvadratini chiqarish.

$$x^{2}+8x+16=-1510+16$$

-1510 ni 16 ga qo'shish.

$$x^{2}+8x+16=-1494$$

x^{2}+8x+16 omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x+4\right)^{2}=-1494$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{-1494}$$

Qisqartirish.

$$x+4=3\sqrt{166}i x+4=-3\sqrt{166}i$$

Tenglamaning ikkala tarafidan 4 ni ayirish.

$$x=-4+3\sqrt{166}i x=-3\sqrt{166}i-4$$